-- particles

Dr. George Krait

Research & Development Engineer

Nancy, France

PhD in Computer Science, specialized in Computational Geometry and Computer Algebra, focusing on problems appearing in visualization tasks and robotics design, with additional interests in Machine Learning.

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Who is This guy?

George Krait, a mathematician and Computer scientist (Computational Geometry) with additional interests in Machine learning. I work as a Research Engineer at the French Institute for Research in Computer Science and Automation, France.

In my Ph.D. program, I was working in (efficiently) plotting singular plane curves preserving properties such as topology . Isolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods are efficient but not certified in general. The goal of my work is to develop certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. This type of curves appears naturally in robotics applications and scientific visualization. In this setting, we show that the singularities can be encoded by a regular square system whose solutions can be isolated with certified numerical methods. Our analysis is conditioned by assumptions that we prove to be generic using Transversality theory . We also provide a semi-algorithm to check their validity. Finally, we present experiments in visualization and robotics, some of which are not reachable by other methods, and discuss the efficiency of our method.

In my master's program at TU Kaiserslautern, Germany I worked in computing a minimal standard basis of an algebraic object called Algebroid curve. I implemented the algorithm and its applications in Singular which is a computer algebra system for polynomial computations.

Resume - Personal Info

General Background
Computational Geometry
95%
Symbolic Computing
95%
Algorithm Development
90%
Algebraic Geometry
85%
Numerical Computing
90%
Programming Skills
Python
85%
Maple
80%
Singular
90%
Matlab
70%
C++
45%
Other skills
Scientific writing (Mathematics & Computer Science)
80%
Latex
80%
Git
70%
MS Office
70%
Language Skills
Arabic
99%
English
90%
German
80%
French
60%
Further Education
  • Machine Learning Jan 2020
    Stanford University \ Coursera

    - Supervised learning (parametric/non-parametric algorithms, support vector machines, kernels, neural networks).

    - Unsupervised learning (clustering, dimensionality reduction, recommender systems, deep learning).

    - Best practices in machine learning (bias/variance theory; innovation process in machine learning and AI).

  • Databases: Advanced Topics in SQL Sep 2020
    Stanford University \ edX

    Indexes and Transactions, Constraints and Triggers,Views and Authorization

  • Databases: Modeling and Theory Jun 2020
    Stanford University \ edX

    Relational Databases, Relational Algebra, Design Theory and Unified Modeling Language

My Resume
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Experience
  • Research & Development Eng Feb 2021 - Ongoing
    French Institute for Research in Computer Science and Automation

    - Designing a fragment of TLA++ capable of being translated into Cubicle

    - Implement translation algorithms from the fragment identifier to Cubicle input language

    - Coupling TLAPS with automatic verification tools using these translations

    - Generating a documentation for the techniques and the produced codes

    Teaching Assistant Sep 2019 - Feb 2021
    University of Lorraine

    Tutoring courses in:

    - Scientific Programming Languages

    - Rational Database


Education
  • Ph.D in Computer Science Nov 2017 - Feb 2021
    French Institute for Research in Computer Science and Automation

    - Pursuing research in modeling the projections of 3D (even higher!) curves.

    - Using efficient symbolic and certified numerical tools for visualization & robotics purposes

    - Designing & implementing related algorithms

    Master in Science (Mathematics) May 2015 -Oct 2017
    TU Kaiserslautern, Germany

    Specialization: Geometry, Algebra and Computer Algebra

    Thesis context: Development and implementation of algorithms regarding curves defined with infinite series

    Bachelor in Mathematics Sep 2009 -Jun 2014
    Damascus University, Syria

    Undertaking an intensive Bachelor program of Pure & Applied Mathematics courses


Awards
  • KAAD Scholarship award 2015 - 2017
    TU Kaiserslautern

    KAAD Scholarship for pursuing master degree at TU Kaiserslautern, Germany

  • International Mathematical Olympiads for University students 2013
    Damascus University

    Selected for the Syrian team in the International Mathematical Olympiads for University students.

  • National Mathematical Olympiads 2010-2013
    Damascus University

    Top ten ranking in the Syrian National Olympiads of Mathematics for University Students.


Blog - My Blog


  • January 31, 2012
  • Math refs

Quoted from my old blog, here are "few" mathematical references in several branches of mathematics ... Enjoy!

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